diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-02 15:10:50 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-02 15:10:50 +0000 |
| commit | 8e5cae9a9f8edbedc2fb2451d32dc18af89cfa40 (patch) | |
| tree | 078003a6c219d021755bca4cc477f5d82b1c0540 /theories/Numbers/NatInt | |
| parent | 0cb098205ba6d85674659bf5d0bfc0ed942464cc (diff) | |
NZLog : since spec is complete, no need for morphism axiom log2_wd
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13608 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/NatInt')
| -rw-r--r-- | theories/Numbers/NatInt/NZLog.v | 12 |
1 files changed, 11 insertions, 1 deletions
diff --git a/theories/Numbers/NatInt/NZLog.v b/theories/Numbers/NatInt/NZLog.v index 34c57aad9..4c8dcc8f3 100644 --- a/theories/Numbers/NatInt/NZLog.v +++ b/theories/Numbers/NatInt/NZLog.v @@ -18,7 +18,6 @@ End Log2. Module Type NZLog2Spec (A : NZOrdAxiomsSig')(B : Pow' A)(C : Log2 A). Import A B C. - Declare Instance log2_wd : Proper (eq==>eq) log2. Axiom log2_spec : forall a, 0<a -> 2^(log2 a) <= a < 2^(S (log2 a)). Axiom log2_nonpos : forall a, a<=0 -> log2 a == 0. End NZLog2Spec. @@ -74,6 +73,17 @@ Proof. order. Qed. +(** Hence log2 is a morphism. *) + +Instance log2_wd : Proper (eq==>eq) log2. +Proof. + intros x x' Hx. + destruct (le_gt_cases x 0). + rewrite 2 log2_nonpos; trivial. reflexivity. now rewrite <- Hx. + apply log2_unique. apply log2_nonneg. + rewrite Hx in *. now apply log2_spec. +Qed. + (** An alternate specification *) Lemma log2_spec_alt : forall a, 0<a -> exists r, |